The resultant of these forces O P → , O Q → , Q R → , O S → a n d O T → is approximately. . . . . . .N [Take 3 = 1 . 7 , 2 = 1 . 4 . Given i ^ a n d j ^ unit vectors along x, y axis]

F → x = [ 1 0 * 3 2 + 2 0 * 1 2 + 2 0 2 − 1 5 2 − 1 5 3 2 ] = 9 . 2 5 i ^ F → y = [ 1 5 * 1 2 + 2 0 * 3 2 + 1 0 * 1 2 − 1 5 2 − 2 0 2 ] = 5 j ^

The resultant of these forces $\vec{O P}, \vec{O Q}, \vec{Q R}, \vec{O S} a n d \vec{O T}$ is approximately. . . . . . .N

[Take $\sqrt[]{3} = 1.7, \sqrt[]{2} = 1.4 .$ Given $\hat{i} a n d \hat{j}$ unit vectors along x, y axis]

Option 1 - <math> <mrow> <mn>9</mn> <mo>.</mo> <mn>2</mn> <mn>5</mn> <mover accent="true"> <mi>i</mi> <mo>^</mo> </mover> <mo>+</mo> <mn>5</mn> <mover accent="true"> <mi>j</mi> <mo>^</mo> </mover> </mrow> </math>

Option 2 - <math> <mrow> <mn>2</mn> <mo>.</mo> <mn>5</mn> <mover accent="true"> <mi>i</mi> <mo>^</mo> </mover> <mo>−</mo> <mn>1</mn> <mn>4</mn> <mo>.</mo> <mn>5</mn> <mover accent="true"> <mi>j</mi> <mo>^</mo> </mover> </mrow> </math>

Option 3 - <math> <mrow> <mo>−</mo> <mn>1</mn> <mo>.</mo> <mn>5</mn> <mover accent="true"> <mi>i</mi> <mo>^</mo> </mover> <mo>−</mo> <mn>1</mn> <mn>5</mn> <mo>.</mo> <mn>5</mn> <mover accent="true"> <mi>j</mi> <mo>^</mo> </mover> </mrow> </math>

Option 4 - <math> <mrow> <mn>3</mn> <mover accent="true"> <mi>i</mi> <mo>^</mo> </mover> <mo>+</mo> <mn>1</mn> <mn>5</mn> <mover accent="true"> <mi>j</mi> <mo>^</mo> </mover> </mrow> </math>

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Vishal Baghel | Contributor-Level 10

6 months ago

Correct Option - 1

Detailed Solution:

${\vec{F}}_{x} = [10 * \frac{\sqrt[]{3}}{2} + 20 * \frac{1}{2} + \frac{20}{\sqrt[]{2}} - \frac{15}{\sqrt[]{2}} - \frac{15 \sqrt[]{3}}{2}] = 9.25 \hat{i}$